ATLANTA—An American infected with Ebola in Liberia was being treated and monitored in the U.S. on Sunday, as doctors worked to provide care in what will be a crucial few days in his attempt to recover from the deadly disease.

(Ebola virus: Read the Journal's latest article.)

About a week after his first symptoms of Ebola were reported, Kent Brantly, a doctor, was in an Atlanta hospital's special isolation unit. He had arrived...